Reverse-price model

The disposable camera supply chain requires a careful design to in-centivize the customer to take the finished camera to a retail store, coordination agreements to incent the retail store to return the product to the manufacturer, a counter to track use of the components, simple snap design to separate components, sufficient capacity of subsidized labor to break apart the camera, and a competitive pricing model to recover component cost over multiple product generations. In short, all the Four Cs of supply chain management had to be planned carefully to ensure an effective reverse supply chain for the FunSaver cameras. 

The Vasicek model was the first term-structure model described in the academic literature, in Vasicek (1977). It is a yield-based, one-factor equilibrium model that assumes the short-rate process follows a normal distribution and incorporates mean reversion. The model is popular with many practitioners as well as academics because it is analytically tractable—that is, it is easily implemented to compute yield curves. Although it has a constant volatility element, the mean reversion feature removes the certainty of a negative interest rate over the long term. Nevertheless, some practitioners do not favor the model because it is not necessarily arbitrage-free with respect to the prices of actual bonds in the market. 

Y. Y Feng and B. C. Xiao. A continuous-time yield management model with multiple prices and reversible price changes. Management Science, 46(5) 644-657, 2000. 

The price that is paid for the greater generality of the models is twofold, however. First, there is the need for two parameters one expressing the surface renewal and one expressing the thickness of the element. Second, thoe is the mathematical complexity of the expression for the flux, N. Is the price worth paying This question can be partly answered by means of Huang and Kuo s application of the film-penetration model to first-order reactions, both irreversible and reversible [32,12]. 

This model incorporates mean reversion, which is not an imrealistic feature. Mean reversion is the process that describes that when the short-rate r is high, it will tend to be pulled back towards the long-term average level when the rate is low, it will have an upward drift towards the average level. In Vasicek s model, the short-rate is pulled to a mean level 6 at a rate of a. The mean reversion is governed by the stochastic term odW which is normally distributed. Using Equation (3.24), Vasicek shows that the price at time t of a zero-coupon bond of maturity T is given by ... 

When calcnlating option prices in a one-factor model, a frequently made assnmption is that the process is driven by the short rate often with a mean reversion featnre linked to the short rate. There are several popnlar models which fall into this category, for example, the Vasicek model, and the Cox, Ingersoll, and Ross model both of which will be discussed in more detail later. Calculating option prices in a two-factor model involves both the short- and long-term rates linked by a mean reversion process. 

An example will provide an idea of how a variation of one of the models proposed by Hull and White described above by the first of equation (18.12) models can be nsed to price an option on a zero-coupon bond. If the assumptions are made that both P, the reversion rate, and o, the volatility, are constant then the model can be restated as... 

The pricing of a European spread option requires the distribution of the credit spread at the maturity (T) of the option. The choice of model affects the probability assigned to each outcome. The mean reversion factor reflects the historic economic features overtime of credit spreads, to revert to the average spreads after larger than expected movements away from the average spread. 

The pricing of a spread option is dependent on the underlying process. As an example we compare the pricing results for a spread option model, including mean reversion to the pricing results from a standard Black-Scholes model in Exhibit 21.14 and Exhibit 21.15. 

Expiry in Six Months Risk-free rate = 10% Strike = 70 bps Credit spread = 60 bps Volatility = 20% Mean Reversion Model Price Standard Black Scholes Price Difference Between Standard Black Scholes and Mean Reversion Model Price... 

The Monte Carlo method, however, is prone to model risk. If the stochastic process chosen for the underlying variable is unrealistic, so will be the estimate of VaR. This is why the choice of the underlying model is particularly important. The geometric Brownian motion model described above adequately describes the behavior of some financial variables, but certainly not that of short-term fixed-income securities. In the Brownian motion, shocks on prices are never reversed. This does not represent the price process for default-free bonds, which must converge to their face value at expiration. 

A 3-tier reverse logistics network design model while determining prices of financial incentives [12]... 

This is the price for the greater and greater structure of this its (open) part, the problematic locality. In the case of cells we can see the wasting away of the whole organism. Our reverse information-thermodynamic model authorizes us to an awaiting of a stable (moderate) higher body temperature of a patient and, also, a less temperature of the problematic texture (73),... 

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